A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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2answers
72 views

What does coordinate invariance mean?

I would like to really understand what the mathematical as well as Physical meaning of coordinate invariance is. I have pretended to know what this means, but upon thinking a little harder today, I am ...
1
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0answers
47 views

How gravitational waves are exactly produced?

I was thinking about gravitational waves, and I found out that I may have a doubt about their production. Assuming the whole calculations find a wave-like solution to be understood, I was wondering ...
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1answer
93 views

Black hole merger orbital speed

If a ship is close to a black hole and we see it getting slower to the point if could see them not for red shift would almost stop moving. Then how fast is the little black hole moving in this video? ...
3
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1answer
128 views

Repeated index in covariant derivative using abstract index notation

The same index showing up twice in the charge conservation law $\nabla_a j^a = 0$, as stated using abstract index notation, highly confuses me. If we chose a coordinate basis ...
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2answers
75 views

What is the metric tensor for?

I am wondering how to use the metric tensor, in practice? I read the book and done the exercises in A student's guide to vectors and tensors by Dan Fleisch. The concept of a tensor and their ...
3
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2answers
198 views

The ADM Energy of Gravitational Waves?

I have been looking for books about this question for several days. However, almost all books use Landau–Lifshitz pseudotensor to calculate the energy of Gravitational Waves.And they said the result ...
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0answers
28 views

Weyl Transformations and Group actions [migrated]

I have the following question. Let $(M,g_{ab})$ be a Riemannian manifold $M$ with metric $g$, and with an action of a Lie group $G$. Moreover, the Riemannian metric $g_{ab}$ is taken to be invariant ...
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1answer
27 views

Inverse gauge transformation in general relativity [closed]

Can someone explain to me how (8.21) follows from (8.20). The Picture comes from A first course in general relativity (Schutz). Thanks and regards, Jens Wagemaker
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1answer
77 views

Why do we introduce the idea of manifold in GR books

After reading Timaeus answer here: http://math.stackexchange.com/questions/1302672/compound-map-in-manifolds, I got an idea that spacetime we usually talk about in GR can be described as a manifold. ...
3
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3answers
494 views

Clarifying what metric counts as flat space

In (2D) Cartesian coordinates, the Euclidean metric... $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$ ...is flat space. If the diagonal elements are exchanged for other real numbers ...
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3answers
593 views

Using a black hole as a mirror

http://www.youtube.com/watch?v=ENd8Sz0AFOk The YouTube video is a good example how the gravity of this merging binary black holes bend light around themselves.
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1answer
47 views

Is there inflationary solution in $R^2$ theory in Jordan frame?

In the Starobinsky $R^2$ inflation model, one usually uses a conformal transformation from Jordan frame to Einstein frame in which the action can be written just like Einstein action + scalar field ...
3
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1answer
191 views

Closed timelike curves in the spin-2 gravity formalism

Let's say we take some topologically trivial CTC spacetime, like the Gödel metric: $$ds^2 = -dt^2 - 2e^{\sqrt{2}\Omega y} dt dx - \frac{1}{2}e^{\sqrt{2}\Omega y} dx^2 + dy^2 + dz^2$$ And then I ...
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2answers
165 views

Timelike Boundary

I was reading in a paper (see 1st paragraph of introduction section in http://arxiv.org/pdf/1510.00709.pdf) that in AdS space, waves can reach the boundary in finite time and, since said boundary is ...
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0answers
21 views

Comoving and physical momentum in a Friedmann universe

It is most probably a very basic question, but I'm a bit stuck with it. Let us consider a spatially flat Friedmann universe with the usual metric ...
2
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1answer
118 views

The Einstein-Cartan equation as the “living heart of gravity”?

I recently read in A Journey into Gravity by Wheeler that "The Einstein-Cartan equation gives us the most vivid image that mankind has ever won of the living heart of gravity" (P.118) ...
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2answers
1k views

Is time going backwards beyond the event horizon of a black hole?

For an outside observer the time seems to stop at the event horizon. My intuition suggests, that if it stops there, then it must go backwards inside. Is this the case? This question is a followup ...
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1answer
101 views

Why pseudo-Riemannian metric cannot define a topology?

It is not clear for me why a positive definite metric is necessary to define a topology as noted in some textbooks like the one by Carroll. Does this imply that in cosmology, say through FLRW metric, ...
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0answers
32 views

Why is spacetime curved by mass but not charge [duplicate]

According to general relativity theory, the deformation of spacetime is proportional to energy tensor $$T_{\mu\nu}.$$ $$ R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi G T_{\mu\nu}. $$ Does it mean that ...
3
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1answer
801 views

$N$-body simulation in General Relativity

How would one perform an $N$-body simulation in General Relativity (GR) for something like galaxy formation or galactic dynamics? Suppose one wants to simulate the rotation curve $v(r)$ for galaxies ...
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2answers
91 views

Redshift of distant galaxies: why not a doppler effect?

How can I explain to my 17 year old pupils that the observed redshift of distant galaxies cannot be interpreted as a doppler effect and inescapably leads to the conclusion that space itself is ...
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0answers
43 views

Direction of Gravity [duplicate]

I ran into a pde that has a parameter in it that can be either $+1$ or $-1$. They say the $+1$ case corresponds to gravity pointing upwards, whereas the $-1$ case applies to gravity pointing ...
15
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4answers
646 views

The problem of self-force on point charges

Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, ...
3
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2answers
282 views

Communication back in time?

On the wikipedia page for time travel, it mentions that Robert Forward said (theoretically, unknown since we don't have a working theory of quantum gravity) that if a heavy nucleus was subjected to an ...
3
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2answers
72 views

Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
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2answers
94 views

Gravitational lensing and perspective

When looking at a black hole the ability to see ourselves is compromised by the small window for the light trajectory to come back to us. The light from the Earth that is bent by (almost) 180° and ...
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1answer
78 views

Time independent Kerr metric

The Kerr metric expressed in terms of polar coordinates $r,\theta,\phi$, such that $x = r\sin(\theta)\cos(\phi)$, $y = r\sin(\theta)\sin(\phi)$, $z = r\cos(\theta)$. Then the Kerr metric is given as ...
4
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1answer
330 views

Wave packet in curved spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
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0answers
36 views

Is it possible to define a symmetry group for the Einstein metric?

I was just wondering if there exists a group of transformations that act on the metric such that the EFE are invariant. At first I thought it would be the group of 2nd roots of unity. That is, the set ...
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4answers
136 views

Which tensor describes curvature in 4D spacetime?

I heard these two statements which don't work together (in my mind): In 4D spacetime the curvature is encoded within the Riemann tensor. He holds all the information about curvature in spacetime. ...
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3answers
169 views

Path of light as it travels between two black holes

What would happen to light passing through a narrow space between the event horizons of two equal-mass black holes? Would it deviate or follow a straight path?
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2answers
553 views

2D space-time curvature [closed]

Actually, why is the space-time curvature considered 2D plane. As 2-D dimensional space-time curve is used to explain why moon revolves around the earth stating because the massive objects wraps the ...
6
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1answer
134 views

Homotopy proof of the lack of foliation of the Gödel metric

A common proof of the lack of foliation of the Gödel universe, apparently mostly copy pasted from Hawking and Ellis, goes thusly : A closed timelike curve must cross a spacelike hypersurface ...
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1answer
91 views

Bigger Galaxies = Faster Clocks [closed]

There are in all about 100 known galaxies with blueshifts out of the billions of galaxies in the observable universe. We have Blue-shifted galaxies are in our own local group, and are all bound to ...
0
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2answers
89 views

Why does a light wave fade as it travels through space?

It stands to reason: if it didn't, the entire sky would be covered with stars shining blindingly day and night. But what causes a light wave (or an electromagnetic wave) to fade if there are no ...
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1answer
37 views

Equation of state in General Relativity versus microscopic description of the fluid

I can't find the answer to the following question. Consider matter fields in General Relativity, assume it to be a perfect fluid. Then its equation of state is, by definition: $$ w=\frac{p}{\rho} = ...
3
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1answer
1k views

What bends fabric of space-time?

I know that mass can bend fabric of space-time, which causes gravity by making an object curve around a planet or star but is there anything else that can bend it? Other energy sources, forces ...
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1answer
124 views

How long ago, and how far away, could “A long time ago in a galaxy far, far away” have been? [closed]

Assume an event happened "A long time ago in a galaxy far, far away", and assume this event includes intelligent carbon-based life forms. What are bounds$^{a}$ on the time and distance (from us) of ...
1
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0answers
173 views

Gravitational lensing on galaxy cluster with given potential

I am having a problem with gravitational lensing question where we are interested in deflection angle of light traveling in potential of galactic cluster, described with tensor ...
1
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1answer
39 views

What is the property which flows as described by the stress energy tensor in GR?

I found the following definitions: The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of ...
3
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0answers
47 views

What is the inertial mass of a black hole?

Or the inertial mass of any spherically symmetric object, can I calculated by measuring very accurately the spacetime distortion this object produces in its surroundings? With 'inertial mass' I mean ...
0
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1answer
51 views

Acceleration of a static observer in Schwarzschild measured in locally inertial frame [closed]

Consider a static observer at $r=R>2M$ with four velocity given by $$U^\mu=\frac{dx^\mu}{d\tau}=(1-\frac{2M}{R})^{-1/2}\delta^\mu_0$$ in the Schwarzschild metric ...
0
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3answers
98 views

How does a mass create the gravitational field of GR? [closed]

As far as I understand, and please correct me if I am wrong, but the basic idea of general relativity is that spacetime is curved by matter. What we call gravity is then not a force as per Newton but ...
5
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1answer
107 views

Simple metric of stellar collapse

Is there a simple metric (Lorentzian manifold) known which exhibits the formation of a black hole while not having any white hole counterpart and which moreover satisfies the strong and dominant ...
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2answers
84 views

When sitting on a chair is it the chair actually pushing against me?

I was listening to The Infinite Monkey Cage on the BBC and they were talking about general relativity and gravity. They were saying that gravity is not a force as Newtonian laws describe and is at ...
4
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3answers
2k views

Equation of everything

Is this equation in the image true? Can you give some topics that I can cover the equation? Similar equation from http://www.preposterousuniverse.com:
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0answers
96 views

How to understand the relationship between these two geometrical structures?

During my study of quantum information processing, I occasionally meet two different geometrical structures: (a) The geometry of the Hilbert space of quantum state, where the superposition and ...
0
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0answers
48 views

Could we have blue/violet shifting?

As the universe expands, it stretches light into longer wavelengths, resulting in what we know as red shifting. But some say that there is a chance in which the universe will stop expanding and then ...
0
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2answers
112 views

Is causality a total order?

I've read that it is physically not possible to violate causality defined as a total order on the spacetime graph. So I was wondering if at least causality can be broked down to a partial order and if ...